The function is .
Fundamental theorem of calculus :
\If is continuous on
, then the function
is defined by
is continuous on
and differentiable on
, then
.
Here .
.
.
Find the critical points by equating .
.
Critcal points are and
.
The test intervals are ,
and
.
\
Interval \ | Test Value | Sign of ![]() | Conclusion |
![]() | ![]() | ![]() | Decreasing |
![]() | ![]() | ![]() | \
Increasing \ |
![]() | ![]() | ![]() | Decreasing |
The function is increasing on the interval .
The function is increasing on the interval .